desperate need of LOTS of help!

[afro_chiq]

ok i have a few problems for calculus 1. my friend that was supposed to help me is nowhere to be found, so in desperation i've turned to the internet. if you can help me on any of these it would be GREATLY APPRECIATED

Comments

[xyresic]

Hahaha, thomsonnow? I'm doing the same thing. I HATE IT.

[xyresic]

Oh, sweet, you're in Gainesville too. Good luck, I just posted some of my own questions too.

[misteral]

These questions involve maximising or minimising some variable. I'd suggest solving them using the following procedure.

Step 1. Form any algebraic expression for the thing you're trying to maximise/minimise. Don't worry if this expression contains lots of other variables at this stage.
Step 2. Use whatever other information or restrictions exist to make substitutions so that you can write your expression in terms of just one variable.
Step 3. Differentiate. Set this derivative equal to zero. Solve.

So you can see an example, I'll do (most of) question 1 for you.

Step 1. We want to maximise the area of the window, so let's form an expression for the total area. Call the height of the rectangle h and the radius of the semicircle r. (So the width of the rectangle is 2r.) This gives us an area, A, as follows...

A = 2rh + ½πr2

Step 2. Now we need to put this all in terms of one variable so let's try and eliminate h. Since we know the perimeter is 24 feet, we have the relationship...

2r + 2h + πr = 24

Rearrange this...

h = ½(24 - 2r